<!DOCTYPE html>
<html>
<head><meta name="generator" content="Hexo 3.9.0">
  <meta charset="utf-8">
  
  <title>NSGA-II 算法学习 | 探花需拔根</title>
  <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1">
  
    <meta name="keywords" content="Bluarry,bluarry,Blog,探花,拔根,博客,区块链,算法,acm">
  
  <meta name="description" content="简介: 此文章是学习进化算法NSGA-II时的学习笔记">
<meta name="keywords" content="自然计算">
<meta property="og:type" content="article">
<meta property="og:title" content="NSGA-II 算法学习">
<meta property="og:url" content="/2019/12/20/2019-12-20-NSGA-II_算法学习/index.html">
<meta property="og:site_name" content="探花需拔根">
<meta property="og:description" content="简介: 此文章是学习进化算法NSGA-II时的学习笔记">
<meta property="og:locale" content="zh.yml">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/image-20191220111947268.png">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/image-201912201130.png">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/2019-12-20-11.43.46.png">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/2019-12-20-2.13.40.png">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/WX20191220-151715.png">
<meta property="og:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/WX20191220-155036.png">
<meta property="og:image" content="">
<meta property="og:image" content="">
<meta property="og:image" content="">
<meta property="og:image" content="">
<meta property="og:image" content="">
<meta property="og:image" content="">
<meta property="og:updated_time" content="2020-03-04T14:58:53.000Z">
<meta name="twitter:card" content="summary">
<meta name="twitter:title" content="NSGA-II 算法学习">
<meta name="twitter:description" content="简介: 此文章是学习进化算法NSGA-II时的学习笔记">
<meta name="twitter:image" content="https://cdn.bluarry.top/wp-content/uploads/2019/12/image-20191220111947268.png">
  
  
    <link rel="icon" href="/favicon.ico">
  
  <link href="//cdn.bootcss.com/font-awesome/4.7.0/css/font-awesome.min.css" rel="stylesheet" type="text/css">
  <link rel="stylesheet" href="/css/style.css">
  <script src="/js/pace.min.js"></script>
  

  
  

  
<!-- Matomo -->
<script type="text/javascript">
	var _paq = window._paq || [];
	/* tracker methods like "setCustomDimension" should be called before "trackPageView" */
	_paq.push(['trackPageView']);
	_paq.push(['enableLinkTracking']);
	(function() {
	  var u="//matomo.bluarry.top/";
	  _paq.push(['setTrackerUrl', u+'matomo.php']);
	  _paq.push(['setSiteId', '3']);
	  var d=document, g=d.createElement('script'), s=d.getElementsByTagName('script')[0];
	  g.type='text/javascript'; g.async=true; g.defer=true; g.src=u+'matomo.js'; s.parentNode.insertBefore(g,s);
	})();
  </script>
  <!-- End Matomo Code -->

</head>
</html>
<body>
  <div id="container">
      <header id="header">
    <div id="banner"></div>
    <div id="header-outer">
        <div id="header-menu" class="header-menu-pos animated">
            <div class="header-menu-container">
                <a href="/" class="left">
                    <span class="site-title">探花需拔根</span>
                </a>
                <nav id="header-menu-nav" class="right">
                    
                    <a  href="/">
                        <i class="fa fa-home"></i>
                        <span>主页</span>
                    </a>
                    
                    <a  href="/archives">
                        <i class="fa fa-archive"></i>
                        <span>归档</span>
                    </a>
                    
                    <a  href="/friends">
                        <i class="fa fa-envira"></i>
                        <span>友链</span>
                    </a>
                    
                    <a  href="/about">
                        <i class="fa fa-user"></i>
                        <span>关于我</span>
                    </a>
                    
                </nav>
                <a class="mobile-header-menu-button">
                    <i class="fa fa-bars"></i>
                </a>
            </div>
        </div>
        <div id="header-row">
            <div id="logo">
                <a href="/">
                    <img src="/images/avatar/me-130x130.jpg" alt="logo">
                </a>
            </div>
            <div class="header-info">
                <div id="header-title">
                    
                    <h2>
                        清风觅影
                    </h2>
                    
                </div>
                <div id="header-description">
                    
                    <h3>
                        致需极,守静笃
                    </h3>
                    
                </div>
            </div>
            <nav class="header-nav">
                <div class="social">
                    
                        <a title="Home"  href="/">
                            <i class="fa fa-home fa-2x"></i></a>
                    
                        <a title="Github" target="_blank" href="//github.com/bluarry">
                            <i class="fa fa-github fa-2x"></i></a>
                    
                        <a title="mail" target="_blank" href="mailto://bluarry@qq.com">
                            <i class="fa fa-envelope-o fa-2x"></i></a>
                    
                </div>
            </nav>
        </div>
    </div>
</header>
      <div class="outer">
        <section id="main" class="body-wrap"><article id="post-2019-12-20-NSGA-II_算法学习" class="article article-type-post" itemscope itemprop="blogPost">
  <div class="article-inner">
    
      <header class="article-header">
        
  
    <h1 class="post-title" itemprop="name">
      NSGA-II 算法学习
    </h1>
    <div class="post-title-bar">
      <ul>
          
              <li>
                  <i class="fa fa-book"></i>
                  
                      <a href="/categories/默认分类/">默认分类</a>
                  
                      <a href="/categories/经验分享/">经验分享</a>
                  
                      <a href="/categories/学习分享/">学习分享</a>
                  
              </li>
          
        <li>
          <i class="fa fa-calendar"></i>  2019-12-20
        </li>
        <li>
          <i class="fa fa-eye"></i>
          <span id="busuanzi_value_page_pv"></span>
        </li>
      </ul>
    </div>
  

          
      </header>
    
    <div class="article-entry post-content" itemprop="articleBody">
      
            
            <blockquote>
<p>简介: 此文章是学习进化算法NSGA-II时的学习笔记<br><a id="more"></a></p>
</blockquote>
<h1 id="NSGA-II-算法学习总结"><a href="#NSGA-II-算法学习总结" class="headerlink" title="NSGA-II 算法学习总结"></a>NSGA-II 算法学习总结</h1><h2 id="一-NSGA-II-算法流程"><a href="#一-NSGA-II-算法流程" class="headerlink" title="一. NSGA-II 算法流程"></a>一. NSGA-II 算法流程</h2><div align="center">
  <img style="border-radius: 0.3125em;box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/image-20191220111947268.png"><br>
  <div style="color:orange; border-bottom: 1px solid #d9d9d9;display: inline-block;color: #999;padding: 2px;">图一</div>
</div>

<p>算法流程如图一所示，这里不做赘述.</p>
<hr>

<h2 id="二-快速非支配排序"><a href="#二-快速非支配排序" class="headerlink" title="二. 快速非支配排序"></a>二. 快速非支配排序</h2><p>直接用例子来说明:</p>
<ol>
<li>对每个个体记录<br>(1)  $ {N_p} $ (支配个体p的个体数量)<br>(2) $ {S_p} $ (被个体p支配的个体数量)</li>
</ol>
<ul>
<li>如图二所示，</li>
</ul>
<div align="center">
  <img style="border-radius: 0.3125em;
  box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/image-201912201130.png"><br>

  <div style="color:orange; border-bottom: 1px solid #d9d9d9;
  display: inline-block;
  color: #999;
  padding: 2px;">图二</div>
</div>

<ol>
<li>找到 \( {N_p}=0 \) 的个体，作为第一非支配等级的个体，即 Rank=1. 如图三所示:</li>
</ol>
<div align="center">
  <img style="border-radius: 0.3125em;
  box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/2019-12-20-11.43.46.png">
  <br>

  <div style="color:orange; border-bottom: 1px solid #d9d9d9;
  display: inline-block;
  color: #999;
  padding: 2px;">图三</div>
</div>

<ol>
<li><p>对于第一非支配等级中的每一个个体p：\(N_p=N_p-1\)<br>找到\( N_p=0 \)的个体作为第二非支配等级的个体，即Rank=2,如图四所示:</p>
<div align="center">
 <img style="border-radius: 0.3125em;
 box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/2019-12-20-2.13.40.png">
 <br>
 <div style="color:orange; border-bottom: 1px solid #d9d9d9;
 display: inline-block;
 color: #999;
 padding: 2px;">图四</div>
</div>
</li>
<li><p>对于第二支配集, 对\(S_p \)中的每一个个体： \( N_p=N_p-1 \)<br>找到\( N_p=0 \)的个体作为第三非支配等级的个体，即Rank=3</p>
</li>
</ol>
<div align="center">
     <img style="border-radius: 0.3125em;
box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/WX20191220-151715.png">
<br><div style="color:orange; border-bottom: 1px solid #d9d9d9;
    display: inline-block;
    color: #999;
    padding: 2px;">图五</div>
</div>

<p>如此循环下去，直到\( S_p \)为空或者所有的个体都已经遍历。</p>
<h2 id="二-计算拥挤距离"><a href="#二-计算拥挤距离" class="headerlink" title="二. 计算拥挤距离"></a>二. 计算拥挤距离</h2><ul>
<li>拥挤距离: 对于每个非支配等级上的个体，计算与该个体相邻的两个个体组成的矩形的长和宽之和.</li>
<li>边界个体的拥挤距离分配为无穷大. 例如，1，2，3，7，5的拥挤距离是无穷大。这样做的原因是为了保证变价在进化过程中保留下来。</li>
</ul>
<div align="center">
  <img style="border-radius: 0.3125em; box-shadow: 0 2px 4px 0 rgba(34,36,38,.12),0 2px 10px 0 rgba(34,36,38,.08);" src="https://cdn.bluarry.top/wp-content/uploads/2019/12/WX20191220-155036.png"><br>
  <div style="color:orange; border-bottom: 1px solid #d9d9d9;display: inline-block; color: #999;padding: 2px;">图六</div>
</div>

<p>如图六所示,拥挤距离如下：<br><img src="" alt="长公式"><br>式中\( f_1^{\max }\)和\(f_1^{\min }\)代表了\(f_1\)方向上的最大值和最小值</p>
<h2 id="三-拥挤度比较算子与二元锦标赛选择"><a href="#三-拥挤度比较算子与二元锦标赛选择" class="headerlink" title="三. 拥挤度比较算子与二元锦标赛选择"></a>三. 拥挤度比较算子与二元锦标赛选择</h2><ul>
<li>在NSGA-II 算法中，使用基于拥挤度比较算子的二元锦标赛选择来选择父代个体。</li>
<li>随机选择两个个体</li>
<li>拥有更低排序值的个体获胜。例如图六，个体1和个体4比较，个体1获胜</li>
<li>如果两个个体拥有相同的排序值，则拥有更大拥挤距离的个体获胜。例如，如图六，个体4和个体6比较，个体4获胜</li>
<li>若两个个体拥有相同的排序值和相同的拥挤距离，则随机选择一个获胜</li>
</ul>
<h2 id="四-模拟二进制交叉（SBX）"><a href="#四-模拟二进制交叉（SBX）" class="headerlink" title="四. 模拟二进制交叉（SBX）"></a>四. 模拟二进制交叉（SBX）</h2><p>模拟二进制交叉是一种实数编码遗传算法的交叉算子，用于生成二进制交叉的子代。假设两个父代个体分别为\( x<em>{p1} \)和\( x</em>{p2}\) ,则子代个体\( x<em>{01} \)和\( x</em>{o2} \)的产生如下:</p>
<ul>
<li>首先满足式子:<br>$ {x^L} &lt; {x<em>{p1}} &lt; {x</em>{p2}}&lt; {x^U} $</li>
</ul>
<p>对于\( x<em>{o1}\)的产生如下:<br><img src="" alt><br><img src="" alt><br>式中，u: [0,1]之间的随机数, \( \eta _c \):交叉分布指数、对于\(x</em>{o2}\)的产生如下:</p>
<p><img src="" alt><br><img src="" alt></p>
<h2 id="五-多项式变异"><a href="#五-多项式变异" class="headerlink" title="五. 多项式变异"></a>五. 多项式变异</h2><ol>
<li>多项式变异用于在父代个体 \(x_p\) 附近变异产生一个子代个体 \( x_o \)</li>
</ol>
<p><img src="" alt><br><br><br><div align="center">
${x_o} = {x_p} + {\delta _q} \cdot ({x^U} - {x^L})$
</div></p>
<h2 id="六-精英保留策略"><a href="#六-精英保留策略" class="headerlink" title="六. 精英保留策略"></a>六. 精英保留策略</h2><ul>
<li>将父代个体和子代种群合并(保留种群中的精英)</li>
<li>在组合种群中进行非支配排序</li>
<li>计算在相同非支配等级的个体的拥挤度距离</li>
<li>基于非支配等级，以升序方式对个体进行排序</li>
<li>对同一非支配等级，按照拥挤距离进行以降序方式排序</li>
<li>选择排序后的前N个个体，N为种群规模</li>
</ul>



            <div class="post-copyright">
    <div class="content">
        <p>最后更新： 2020年03月04日 22:58</p>
        <p>原始链接： <a class="post-url" href="/2019/12/20/2019-12-20-NSGA-II_算法学习/" title="NSGA-II 算法学习">/2019/12/20/2019-12-20-NSGA-II_算法学习/</a></p>
        <footer>
            <a href="">
                <img src="/images/avatar/me-130x130.jpg" alt="bluarry">
                bluarry
            </a>
        </footer>
    </div>
</div>

      
        
            
<div class="page-reward">
    <a id="rewardBtn" href="javascript:;">赏</a>
</div>

<div id="reward" class="post-modal reward-lay">
    <a class="close" href="javascript:;" id="reward-close">×</a>
    <span class="reward-title">
        <i class="icon icon-quote-left"></i>
        请我吃糖~
        <i class="icon icon-quote-right"></i>
    </span>
    <div class="reward-content">
        
        <div class="reward-code">
            <img id="rewardCode" src="/images/wechat_code.jpg" alt="打赏二维码">
        </div>
        <div class="reward-select">
            
            <label class="reward-select-item checked" data-id="wechat" data-wechat="/images/wechat_code.jpg">
                <img class="reward-select-item-wechat" src="/images/wechat.png" alt="微信">
            </label>
            
            
            <label class="reward-select-item" data-id="alipay" data-alipay="/images/alipay_code.jpg">
                <img class="reward-select-item-alipay" src="/images/alipay.png" alt="支付宝">
            </label>
            
        </div>
    </div>
</div>


        
    </div>
    <footer class="article-footer">
        
        
<div class="post-share">
    <a href="javascript:;" id="share-sub" class="post-share-fab">
        <i class="fa fa-share-alt"></i>
    </a>
    <div class="post-share-list" id="share-list">
        <ul class="share-icons">
          <li>
            <a class="weibo share-sns" target="_blank" href="http://service.weibo.com/share/share.php?url=/2019/12/20/2019-12-20-NSGA-II_算法学习/&title=《NSGA-II 算法学习》 — 探花需拔根&pic=images/avatar/me-130x130.jpg" data-title="微博">
              <i class="fa fa-weibo"></i>
            </a>
          </li>
          <li>
            <a class="weixin share-sns" id="wxFab" href="javascript:;" data-title="微信">
              <i class="fa fa-weixin"></i>
            </a>
          </li>
          <li>
            <a class="qq share-sns" target="_blank" href="http://connect.qq.com/widget/shareqq/index.html?url=/2019/12/20/2019-12-20-NSGA-II_算法学习/&title=《NSGA-II 算法学习》 — 探花需拔根&source=
简介: 此文章是学习进化算法NSGA-II时的学习笔记" data-title="QQ">
              <i class="fa fa-qq"></i>
            </a>
          </li>
          <li>
            <a class="facebook share-sns" target="_blank" href="https://www.facebook.com/sharer/sharer.php?u=/2019/12/20/2019-12-20-NSGA-II_算法学习/" data-title="Facebook">
              <i class="fa fa-facebook"></i>
            </a>
          </li>
          <li>
            <a class="twitter share-sns" target="_blank" href="https://twitter.com/intent/tweet?text=《NSGA-II 算法学习》 — 探花需拔根&url=/2019/12/20/2019-12-20-NSGA-II_算法学习/&via=" data-title="Twitter">
              <i class="fa fa-twitter"></i>
            </a>
          </li>
          <li>
            <a class="google share-sns" target="_blank" href="https://plus.google.com/share?url=/2019/12/20/2019-12-20-NSGA-II_算法学习/" data-title="Google+">
              <i class="fa fa-google-plus"></i>
            </a>
          </li>
        </ul>
     </div>
</div>
<div class="post-modal wx-share" id="wxShare">
    <a class="close" href="javascript:;" id="wxShare-close">×</a>
    <p>扫一扫，分享到微信</p>
    <img src="" alt="微信分享二维码">
</div>

<div class="mask"></div>

        
        <ul class="article-footer-menu">
            
            
  <li class="article-footer-tags">
    <i class="fa fa-tags"></i>
      
    <a href="/tags/自然计算/" class="color5">自然计算</a>
      
  </li>

        </ul>
        
        

    <aside class="post-toc-pos post-toc-top" id="post-toc">
        <nav class="post-toc-wrap">
            <ol class="post-toc"><li class="post-toc-item post-toc-level-1"><a class="post-toc-link" href="#NSGA-II-算法学习总结"><span class="post-toc-text">NSGA-II 算法学习总结</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#一-NSGA-II-算法流程"><span class="post-toc-text">一. NSGA-II 算法流程</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#二-快速非支配排序"><span class="post-toc-text">二. 快速非支配排序</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#二-计算拥挤距离"><span class="post-toc-text">二. 计算拥挤距离</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#三-拥挤度比较算子与二元锦标赛选择"><span class="post-toc-text">三. 拥挤度比较算子与二元锦标赛选择</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#四-模拟二进制交叉（SBX）"><span class="post-toc-text">四. 模拟二进制交叉（SBX）</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#五-多项式变异"><span class="post-toc-text">五. 多项式变异</span></a></li><li class="post-toc-item post-toc-level-2"><a class="post-toc-link" href="#六-精英保留策略"><span class="post-toc-text">六. 精英保留策略</span></a></li></ol></li></ol>
        </nav>
    </aside>
    

<nav id="article-nav">
  
    <a href="/2019/12/27/2019-12-27-linux下搞个utorrent服务器/" id="article-nav-newer" class="article-nav-link-wrap">

      <span class="article-nav-title">
        <i class="fa fa-hand-o-left" aria-hidden="true"></i>
        
          linux下搞个utorrent服务器
        
      </span>
    </a>
  
  
    <a href="/2019/11/18/2019-11-18-linux下常用软件安装的命令/" id="article-nav-older" class="article-nav-link-wrap">
      <span class="article-nav-title">linux下常用软件安装的命令</span>
      <i class="fa fa-hand-o-right" aria-hidden="true"></i>
    </a>
  
</nav>




    <!-- HTML页面布局 -->
    <div id="tab-list">
        <ul id="ul1">
            
            
            
            <li id="gittalk" style="width: 25%;">gittalk</li>
            
            
            <li id="valine" style="width: 25%;">valine</li>
            
        </ul>
         
        
          
        <div id="dv_gitment" class="hide">
            <div id="git_comments"></div>;
        </div>
        
        
        <div id="dv_vment" class="show">
            <div class="comments vcomment" id="vcomments"></div>
        </div>
        
    </div>

    <script src="/js/tablist.js"></script>
   

    
        
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/gitalk@1/dist/gitalk.css">
<script src="https://cdn.jsdelivr.net/npm/gitalk@1/dist/gitalk.min.js"></script>
<script src="https://cdn.bluarry.top/cdn/js/md5.min.js"></script>
<!--<div id="git_comments"></div>-->
<script>
    // var gitment = new Gitment({
    //     owner: 'bluarry',
    //     repo: 'blog_comment',
    //     oauth: {
    //         client_id: '5c95f5b820d109c8f5c1',
    //         client_secret: 'f1cfe5b08f9a55923ba26a9ec8855b631002ad18',
    //     },
    // })
    var hrefs=location.href;
    var links=hrefs.split('/');
    var cr="";
    for (var i=0;i<Math.min(7,links.length);i++) {
        cr+=links[i];
    }
    console.log(cr);

    var gitalk = new Gitalk({
        clientID: '5c95f5b820d109c8f5c1', //Client ID
        clientSecret: 'f1cfe5b08f9a55923ba26a9ec8855b631002ad18', //Client Secret
        repo: 'blog_comment',//仓库名称
        owner: 'bluarry',//仓库拥有者
        admin: ['bluarry'],
        id: md5(cr),      // Ensure uniqueness and length less than 50
        distractionFreeMode: false  // Facebook-like distraction free mode
    });
    gitalk.render('git_comments');
</script>


    
        <!-- Valine Comments -->
<!-- <div class="comments vcomment" id="vcomments"></div>-->
<script src="//cdn1.lncld.net/static/js/3.0.4/av-min.js"></script>
<script src="//unpkg.com/valine@latest/dist/Valine.min.js"></script>
<!-- Valine Comments script -->
<script>
    var GUEST_INFO = ['nick','mail','link'];
    var guest_info = 'nick,mail'.split(',').filter(function(item){
        return GUEST_INFO.indexOf(item) > -1
    });
    new Valine({
        el: '#vcomments',
        notify: 'true' == 'true',
        verify: 'false' == 'true',
        appId: "DRrkhLYTmB6QwGy6sI6vCH8C-gzGzoHsz",
        appKey: "M4A4lrKwbixQmmeO5lVdY5l2",
        avatar: "mm",
        placeholder: "少侠，留下你的评论吧",
        guest_info: guest_info.length == 0 ? GUEST_INFO : guest_info,
        pageSize: "10"
    })
</script>
<!-- Valine Comments end -->

    


    </footer>
  </div>
</article>

  <script type="text/x-mathjax-config">
MathJax.Hub.Config({
    tex2jax: {
        inlineMath: [ ['$','$'], ["\\(","\\)"]  ],
        processEscapes: true,
        skipTags: ['script', 'noscript', 'style', 'textarea', 'pre', 'code']
    }
});

MathJax.Hub.Queue(function() {
    var all = MathJax.Hub.getAllJax(), i;
    for(i=0; i < all.length; i += 1) {
        all[i].SourceElement().parentNode.className += ' has-jax';                 
    }       
});
</script>

<!-- 
    <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML"></script> 
-->

<script type="text/javascript" src="https://res.ailemon.net/mathjax/2.7.5/MathJax.js?config=default&amp;ver=1.3.11"></script>

<!--
<script type="text/javascript" src="https://src.ailemon.me/mathjax/2.7.5/MathJax.js?config=default&amp;ver=1.3.11"></script>
-->



</section>
        
      </div>
      <footer id="footer">
  <div class="outer">
    <div id="footer-info" class="inner">
      
<p>
    <span id="busuanzi_container_site_uv" style='display:none'>
        <i class="fa fa-user"></i>&nbsp;&nbsp;<span id="busuanzi_value_site_uv"></span>
    </span>&nbsp;&nbsp;|&nbsp;&nbsp;
    <span id="busuanzi_container_site_pv" style='display:none'>
        <i class="fa fa-eye"></i> &nbsp;&nbsp;<span id="busuanzi_value_site_pv"></span>
    </span>
</p>


      <p>
      &copy; 2016-2021 &nbsp;&nbsp;<i style="color: red;" class="fa fa-heart"></i>&nbsp;&nbsp; bluarry
      备案号: <a style="color: #999;" href="http://www.beian.miit.gov.cn/" target="_blank">陕ICP备2020012959号</a>
    </p>

    </div>
  </div>
</footer>
    <script async src="//busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
<script src="//cdn.bootcss.com/jquery/3.2.1/jquery.min.js"></script>
<script>
  var mihoConfig = {
      root: "",
      animate: true,
      isHome: false,
      share: true,
      reward: 1
  }
</script>
<div class="sidebar">
    <div id="sidebar-search" title="Search">
        <i class="fa fa-search"></i>
    </div>
    <div id="sidebar-category" title="Categories">
        <i class="fa fa-book"></i>
    </div>
    <div id="sidebar-tag" title="Tags">
        <i class="fa fa-tags"></i>
    </div>
    <div id="sidebar-top">
        <span class="sidebar-top-icon"><i class="fa fa-angle-up"></i></span>
    </div>
</div>
<div class="sidebar-menu-box" id="sidebar-menu-box">
    <div class="sidebar-menu-box-container">
        <div id="sidebar-menu-box-categories">
            <a class="category-link" href="/categories/linux/">linux</a><a class="category-link" href="/categories/linux-学习/">linux 学习</a><a class="category-link" href="/categories/linux-学习-acm-onlinejudge-hustoj/">linux 学习 acm onlinejudge hustoj</a><a class="category-link" href="/categories/学习分享/">学习分享</a><a class="category-link" href="/categories/数据结构/">数据结构</a><a class="category-link" href="/categories/经验分享/">经验分享</a><a class="category-link" href="/categories/经验分享/学习分享/">学习分享</a><a class="category-link" href="/categories/默认分类/">默认分类</a><a class="category-link" href="/categories/默认分类/复习/">复习</a><a class="category-link" href="/categories/默认分类/复习/学习分享/">学习分享</a><a class="category-link" href="/categories/默认分类/学习分享/">学习分享</a><a class="category-link" href="/categories/默认分类/生活杂谈/">生活杂谈</a><a class="category-link" href="/categories/默认分类/经验分享/">经验分享</a><a class="category-link" href="/categories/默认分类/经验分享/学习分享/">学习分享</a>
        </div>
        <div id="sidebar-menu-box-tags">
            <a href="/tags/Java/" style="font-size: 10px;">Java</a> <a href="/tags/acm/" style="font-size: 12.86px;">acm</a> <a href="/tags/android/" style="font-size: 11.43px;">android</a> <a href="/tags/c/" style="font-size: 14.29px;">c++</a> <a href="/tags/fabric/" style="font-size: 11.43px;">fabric</a> <a href="/tags/kali/" style="font-size: 10px;">kali</a> <a href="/tags/linux/" style="font-size: 15.71px;">linux</a> <a href="/tags/linux学习/" style="font-size: 10px;">linux学习</a> <a href="/tags/mac/" style="font-size: 10px;">mac</a> <a href="/tags/mfc/" style="font-size: 10px;">mfc</a> <a href="/tags/onlinejudge/" style="font-size: 10px;">onlinejudge</a> <a href="/tags/sqlite/" style="font-size: 10px;">sqlite</a> <a href="/tags/sqlite3/" style="font-size: 11.43px;">sqlite3</a> <a href="/tags/ss/" style="font-size: 10px;">ss</a> <a href="/tags/vs/" style="font-size: 11.43px;">vs</a> <a href="/tags/xposed/" style="font-size: 10px;">xposed</a> <a href="/tags/xposed模块/" style="font-size: 10px;">xposed模块</a> <a href="/tags/专业知识/" style="font-size: 10px;">专业知识</a> <a href="/tags/侧链/" style="font-size: 10px;">侧链</a> <a href="/tags/内网穿透/" style="font-size: 10px;">内网穿透</a> <a href="/tags/区块链/" style="font-size: 11.43px;">区块链</a> <a href="/tags/复习/" style="font-size: 10px;">复习</a> <a href="/tags/学习/" style="font-size: 18.57px;">学习</a> <a href="/tags/安卓/" style="font-size: 12.86px;">安卓</a> <a href="/tags/小技巧/" style="font-size: 17.14px;">小技巧</a> <a href="/tags/数据库/" style="font-size: 10px;">数据库</a> <a href="/tags/数据结构/" style="font-size: 10px;">数据结构</a> <a href="/tags/日常使用问题/" style="font-size: 10px;">日常使用问题</a> <a href="/tags/最小生成树/" style="font-size: 11.43px;">最小生成树</a> <a href="/tags/最短路径/" style="font-size: 10px;">最短路径</a> <a href="/tags/比特币/" style="font-size: 11.43px;">比特币</a> <a href="/tags/算法/" style="font-size: 12.86px;">算法</a> <a href="/tags/算法笔记/" style="font-size: 11.43px;">算法笔记</a> <a href="/tags/经验/" style="font-size: 20px;">经验</a> <a href="/tags/编译原理/" style="font-size: 10px;">编译原理</a> <a href="/tags/翻译/" style="font-size: 10px;">翻译</a> <a href="/tags/自然计算/" style="font-size: 10px;">自然计算</a>
        </div>
    </div>
    <a href="javascript:;" class="sidebar-menu-box-close">&times;</a>
</div>
<div class="mobile-header-menu-nav" id="mobile-header-menu-nav">
    <div class="mobile-header-menu-container">
        <span class="title">Menus</span>
        <ul class="mobile-header-menu-navbar">
            
            <li>
                <a  href="/">
                    <i class="fa fa-home"></i><span>主页</span>
                </a>
            </li>
            
            <li>
                <a  href="/archives">
                    <i class="fa fa-archive"></i><span>归档</span>
                </a>
            </li>
            
            <li>
                <a  href="/friends">
                    <i class="fa fa-envira"></i><span>友链</span>
                </a>
            </li>
            
            <li>
                <a  href="/about">
                    <i class="fa fa-user"></i><span>关于我</span>
                </a>
            </li>
            
        </ul>
    </div>
    <div class="mobile-header-tag-container">
        <span class="title">Tags</span>
        <div id="mobile-header-container-tags">
            <a href="/tags/Java/" style="font-size: 10px;">Java</a> <a href="/tags/acm/" style="font-size: 12.86px;">acm</a> <a href="/tags/android/" style="font-size: 11.43px;">android</a> <a href="/tags/c/" style="font-size: 14.29px;">c++</a> <a href="/tags/fabric/" style="font-size: 11.43px;">fabric</a> <a href="/tags/kali/" style="font-size: 10px;">kali</a> <a href="/tags/linux/" style="font-size: 15.71px;">linux</a> <a href="/tags/linux学习/" style="font-size: 10px;">linux学习</a> <a href="/tags/mac/" style="font-size: 10px;">mac</a> <a href="/tags/mfc/" style="font-size: 10px;">mfc</a> <a href="/tags/onlinejudge/" style="font-size: 10px;">onlinejudge</a> <a href="/tags/sqlite/" style="font-size: 10px;">sqlite</a> <a href="/tags/sqlite3/" style="font-size: 11.43px;">sqlite3</a> <a href="/tags/ss/" style="font-size: 10px;">ss</a> <a href="/tags/vs/" style="font-size: 11.43px;">vs</a> <a href="/tags/xposed/" style="font-size: 10px;">xposed</a> <a href="/tags/xposed模块/" style="font-size: 10px;">xposed模块</a> <a href="/tags/专业知识/" style="font-size: 10px;">专业知识</a> <a href="/tags/侧链/" style="font-size: 10px;">侧链</a> <a href="/tags/内网穿透/" style="font-size: 10px;">内网穿透</a> <a href="/tags/区块链/" style="font-size: 11.43px;">区块链</a> <a href="/tags/复习/" style="font-size: 10px;">复习</a> <a href="/tags/学习/" style="font-size: 18.57px;">学习</a> <a href="/tags/安卓/" style="font-size: 12.86px;">安卓</a> <a href="/tags/小技巧/" style="font-size: 17.14px;">小技巧</a> <a href="/tags/数据库/" style="font-size: 10px;">数据库</a> <a href="/tags/数据结构/" style="font-size: 10px;">数据结构</a> <a href="/tags/日常使用问题/" style="font-size: 10px;">日常使用问题</a> <a href="/tags/最小生成树/" style="font-size: 11.43px;">最小生成树</a> <a href="/tags/最短路径/" style="font-size: 10px;">最短路径</a> <a href="/tags/比特币/" style="font-size: 11.43px;">比特币</a> <a href="/tags/算法/" style="font-size: 12.86px;">算法</a> <a href="/tags/算法笔记/" style="font-size: 11.43px;">算法笔记</a> <a href="/tags/经验/" style="font-size: 20px;">经验</a> <a href="/tags/编译原理/" style="font-size: 10px;">编译原理</a> <a href="/tags/翻译/" style="font-size: 10px;">翻译</a> <a href="/tags/自然计算/" style="font-size: 10px;">自然计算</a>
        </div>
    </div>
</div>
<div class="search-wrap">
    <span class="search-close">&times;</span>
        <a href="javascript:;" class="header-icon waves-effect waves-circle waves-light" id="back">
            <i class="icon icon-lg icon-chevron-left"></i>
        </a>
        <input class="search-field" placeholder="Search..." id="keywords">
        <a id="search-submit" href="javascript:;">
            <i class="fa fa-search"></i>
        </a>
    <div class="search-container" id="search-container">
        <ul class="search-result" id="search-result">
        </ul>
    </div>
</div>

<div id="search-tpl">
    <li class="search-result-item">
        <a href="{url}" class="search-item-li">
            <span class="search-item-li-title" title="{title}">{title}</span>
        </a>
    </li>
</div>
<script src="/js/search.js"></script>
<script src="/js/main.js"></script>


  <script src="//cdn.bootcss.com/particles.js/2.0.0/particles.min.js"></script>
  <div id="particles"></div>
  <script src="/js/particles.js"></script>







  <link rel="stylesheet" href="//cdn.bootcss.com/animate.css/3.5.0/animate.min.css">
  <script src="//cdn.bootcss.com/scrollReveal.js/3.0.5/scrollreveal.js"></script>
  <script src="/js/animate.js"></script>


  <script src="/js/pop-img.js"></script>
  <script>
     $(".article-entry p img").popImg();
  </script>

  </div>
</body>
</html>